For any positive integer n, $$s(n)$$ is the sum of the digits of n. What is the minimum value of $$\frac{n}{s(n)}$$ when (1) $$10 \le n \le 99$$ and (2) $$100 \le n \le 999$$?

To minimize $$\frac{n}{s(n)}$$, we want n as small as possible relative to a large digit sum. For two-digit numbers, checking candidates shows $$n=19$$ with $$s(n)=10$$ gives the minimum ratio $$\frac{19}{10}=1.9$$. For three-digit numbers, checking candidates similarly shows $$n=199$$ with $$s(n)=19$$ gives the minimum ratio $$\frac{199}{19} \approx 10.4736842$$.